X3157

X1-CEVA CONJUGATE OF X3

X3157 = isogonal conjugate of X7040
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 3, 73 }: Central Line L(3, 73) { 12, 68 }: Central Line L(12, 68) { 1, 90 }: Central Line L(1, 90) { 6, 169 }: Central Line L(6, 169) { 56, 215 }: Central Line L(56, 215) { 72, 394 }: Central Line L(72, 394) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_215 = -CEVA CONJUGATE OF X(50) (0.4113, 0.3887) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_3157 = -CEVA CONJUGATE OF X(3) (0.7579, 0.3180) A B C X1 X3 X73 X12 X68 X90 X6 X169 X56 X215 X72 X394 X3157 (a, b, c) = (5, 6, 7) | AB = 1

X3157 (X1-CEVA CONJUGATE OF X3) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X1 and \(u : v : w\) = X3
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(1.327500355442\)
▸ Incident Central Lines27 lines

{1, 90}, {3, 73}, {6, 169}, {12, 68}, {31, 1066}, {40, 1419}, {46, 1079}, {55, 500}, {56, 215}, {65, 921}, {72, 394}, {221, 517}, {495, 611}, {602, 1458}, {916, 2293}, {971, 1498}, {999, 1201}, {1062, 1071}, {1064, 1496}, {1068, 3193}, {1092, 1425}, {1339, 1616}, {1433, 1807}, {1480, 3057}, {1745, 1936}, {1854, 2771}, {1870, 1993}

▸ Functional Relations3 relations